Mom says we can't eat with our hands when we're out.
Would most Americans use 'can't' here or would they prefer 'we're not allowed to' or 'mustn't', would you think?
"can't" is OK. So is "not allowed". I wouldn't say "mustn't".
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anonymouswould they prefer 'we're not allowed to' or 'mustn't'
I would use shouldn't. There are certain foods though that we can eat with our hands and be polite. There is a name for them - "finger foods".